Problem preview

G-CO.11 Warmup M2-035-A10-V02

Prove parallelogram theorems and their converses, including diagonal and rectangle results.

Test the diagonal-bisection converse for a parallelogram

Problem

Decide whether the diagonal evidence is sufficient to prove a parallelogram: quadrilateral \(ABCD\); diagonals \(AC\) and \(BD\) intersect at \(M\) with \(AM=CM\) and \(BM=DM\).

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Sufficient because AM = CM; BM = DM is not needed.

Sufficient because AM = CM and BM = DM, even if they do not share midpoint M.

Sufficient because AC = BD.

Sufficient. AM = CM and BM = DM at common point M, so the diagonals bisect each other.

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Curriculum context

Course: Math II
Standard: G-CO.11
Category: Geometry
Domain: Congruence
Objective: Prove parallelogram theorems and their converses, including diagonal and rectangle results.
Problem type: Test the diagonal-bisection converse for a parallelogram